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Apostol exercise

  1. Apr 22, 2005 #1
    Hello! Anyone read Apostol's Calculus vol. 1. On p. 28 the exercises feels very hard. Can somebody help me with nr. 2?
     
  2. jcsd
  3. Apr 22, 2005 #2
    can u post the prob. here?
     
  4. Apr 22, 2005 #3
    I thought it would be useless because the answer must build on his axioms...
    But here it comes:
    If x is an arbitrary real number, prove that there exist postive integers such as m<x<n.
     
  5. Apr 22, 2005 #4
    do you mean m < abs(x) < n?
     
  6. Apr 23, 2005 #5

    honestrosewater

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    And what if x = 0? danne89, what is the problem, word-for-word?
     
  7. Apr 23, 2005 #6
    The problem states that if x is an arbitary real number, then there exist integers m and n such that m < x < n. The problem makes no reference to positive or otherwise. No wonder you're having such a hard time with the problem.
     
  8. Apr 23, 2005 #7

    honestrosewater

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    The negation says that there exists a real number x such that, for all integers m and n, (m > x) or (x > n). IOW, that the set of integers is bounded below or bounded above or both. Is that true?
     
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